Seriously, do a search for best Cary Grant movies and go seek some out; even though nobody can agree on the order of said lists, everyone agrees which movies should be on there.
I actually know Cary Grant very well, you could say I'm a bit of a fan. When DVDs were a thing (giving you a hint about my age) I bought lots of his movies. So I can truly second the recommendations mentioned in the other answers here.
But I wouldn't have been surprised if knowledge of someone like Cary Grant couldn't be generally expected from the average tech audience of today, although I believe that they are on average more knowledgeable about and interested in general (everyday) culture. I mean, there has been more than one instance where I heard a younger colleague talk passionately about how much they liked a certain movie or show which I also love - only to find out that they are actually talking about a recent remake that I had never heard of. So not everything can be taken for granted.
His name appears in dozens of song lyrics[1], many of them from after his death. Many are in other languages, and he's often paired with a similarly famous female star (Bette Davis, Audrey Hepburn).
I suspect many people have heard of him even if they can't name a single film he was in.
Ha! First, let’s not forget. Grant was a “movie star”. But seriously, he was a star from a time even before I was born.
The difference probably has to do with the difference between people who grew up during the ages of broadcast television, cable television, video rentals (prolly add PC video games here), internet entertainment, and internet ‘television’.
If you grew up in the age of broadcast television you watched everything or went outside.
As an aside, I was talking to an intern at work. Somehow movies were mentioned and I guess I cited a quote from Pulp Fiction (1994).
Me: Oh? You haven’t seen it? It’s a great movie.
Intern: I don’t watch old movies.
(>_<)
That said, check out Charade. It's amazing.
EDIT: crap, no, 45 is right.
Had this been asked few months ago I'd probably gave the same answer.
That's said, have some kindness for us. Masterpieces are getting undeservedly buried under pile of garbage produced by major companies nowadays, so discovering amazing talents is like a breath of fresh air.
Another fun classic is "Arsenic and Old Lace" even though you can very much tell that it's a stage adaptation. My friend's favorite Cary Grant movie is "That Touch of Mink" which I need to see again because the first time I watched it I didn't really get into it.
"Holiday", which is discussed in the original article, is definitely another recommendation worth watching.
And let's not forget the Hitchcock ones, like "North by Northwest", or, my favorite, "To Catch a Thief".
Recommended Arsenic and Old Lace weren't enjoyable at all (Grant played amazingly though), but the Philadelphia Story (best movie I've seen in years), Charade, North by Northwest, Father Goose - those are amazing masterpieces which I enjoyed a lot.
You could try Notorious, and the Holiday - two very different specimen - and see which side you're leaning towards more, for instance.
Happened to see both Notorious and Holiday over the last weekend and thoroughly enjoyed both.